Y = 3(x + 3)(x +1)identify the vertex of the parabola

Question

`y = 3(x + 3)(x +1)`identify the vertex of the parabola

Answer 1

Vertex = (-2,-3).

Step-by-step explanation:

Given the equation of the parabola:

`y=3\mleft(x+3\mright)\mleft(x+1\mright)`

First, we find the axis of symmetry using the formula:

`\begin{gathered} x=(r+s)/(2)\text{ (r and s are the zeros)}\colon r=-3,s=-1 \\ x=(-3-1)/(2) \\ x=-(4)/(2) \\ x=-2 \end{gathered}`

Next, determine the value of y at x=-2:

`\begin{gathered} y=3\mleft(x+3\mright)\mleft(x+1\mright) \\ y=3\mleft(-2+3\mright)\mleft(-2+1\mright) \\ =3(1)(-1) \\ y=-3 \end{gathered}`

Thus. the vertex of the parabola is (x,y)=(-2,-3).